The development of new statistical models for the meta-analysis of diagnostic test accuracy studies is still an ongoing field of research, especially with respect to summary receiver operating characteristic (ROC) curves. In the recently published updated version of the "Cochrane Handbook for Systematic Reviews of Diagnostic Test Accuracy", the authors point to the challenges of this kind of meta-analysis and propose two approaches. However, both of them come with some disadvantages, such as the nonstraightforward choice of priors in Bayesian models or the requirement of a two-step approach where parameters are estimated for the individual studies, followed by summarizing the results. As an alternative, we propose a novel model by applying methods from time-to-event analysis. To this task we use the discrete proportional hazard approach to treat the different diagnostic thresholds, that provide means to estimate sensitivity and specificity and are reported by the single studies, as categorical variables in a generalized linear mixed model, using both the logit- and the asymmetric cloglog-link. This leads to a model specification with threshold-specific discrete hazards, avoiding a linear dependency between thresholds, discrete hazard, and sensitivity/specificity and thus increasing model flexibility. We compare the resulting models to approaches from the literature in a simulation study. While the estimated area under the summary ROC curve is estimated comparably well in most approaches, the results depict substantial differences in the estimated sensitivities and specificities. We also show the practical applicability of the models to data from a meta-analysis for the screening of type 2 diabetes.